To determine the correct statement regarding Antonio and Candice's race, we need to analyze the information given.
Antonio's Data Analysis:
From the table, we can observe Antonio's distance at various times:
- At 8 seconds: 29 meters
- At 12 seconds: 41 meters
- At 16 seconds: 53 meters
- At 20 seconds: 65 meters
- At 24 seconds: 77 meters
We can calculate the slope (rate of distance per second) of Antonio's movement. The difference in distance over the difference in time gives:
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From 8 seconds (29m) to 12 seconds (41m): \( \text{Distance change} = 41 - 29 = 12 \) meters \( \text{Time change} = 12 - 8 = 4 \) seconds
Rate = \( \frac{12}{4} = 3 \) meters/second
This rate remains consistent throughout, indicating that Antonio runs at a constant speed of 3 meters per second.
Candice's Data Analysis:
For Candice, we have points through which a line passes:
- (5, 22)
- (10, 42)
- (15, 62)
- (20, 82)
Let's calculate the distance Candice covers per second:
From (5, 22) to (10, 42):
- Distance change: \( 42 - 22 = 20 \) meters
- Time change: \( 10 - 5 = 5 \) seconds
Rate = \( \frac{20}{5} = 4 \) meters/second.
This indicates that Candice is moving at a speed of 4 meters per second.
Head Start Calculation:
Now, to determine who had a head start, we need to compare their distances at the same time.
Let's find the distance that Candice would have covered at 8 seconds:
Using Candice’s speed of 4 meters/second:
Distance at 8 seconds = \( 4 \times 8 = 32 \) meters.
At 8 seconds, Antonio has traveled 29 meters. Thus, Candice is already ahead:
- Candice Distance (8 seconds): 32 meters
- Antonio Distance (8 seconds): 29 meters
This indicates that Candice had a head start of:
\( 32 - 29 = 3 \) meters.
Conclusion:
Candice had a head start of 3 meters, so the correct statement is:
Candice had a head start of 3 meters.
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